Similar to the mean-field case, the dissipation potential consists of relative entropies with respect to geometric averages, now of forward and backward rates along a transition \(\nu \rightarrow \nu \pm \genfrac{}{}{}2{1}{n}\delta _{x}\) .
Moreover, note that in contrast to the framework of [1]}, we employ fluxes \(\mathsf {J}^{\pm }\)  that are not finite measures. This is due to the unboundedness of \(\kappa _{\nu }\)  as the mass of \(\nu \)  grows, which implies that the underlying jump kernel over \(\Gamma \)  is itself unbounded as well, see Section .
